Question

a quadratic function f(x) is given below f(x)=2.6x²+bc+c suppose that f(x) has a y intercept value oof 4.1 and that the point p (5, 87.6) is on theparabolic graph of y=f(x) determine the exact numeric value of b and c?

Answer 1

To determine the values of b and c for the quadratic function f(x) = 2.6x² + bx + c, the y-intercept gives c = 4.1, and substituting the point (5, 87.6) into the function and solving for b yields b = 3.7.

Step-by-step explanation:

The quadratic function is given as f(x) = 2.6x² + bx + c. To find the values of b and c, we use the information provided:

• The y-intercept is at 4.1, which means f(0) = c = 4.1.
• The point (5, 87.6) lies on the graph, so f(5) = 2.6·(5)² + b·5 + 4.1 = 87.6.

Solving the equation 2.6·(5)² + b·5 + 4.1 = 87.6 gives us:

65 + 5b + 4.1 = 87.6
5b = 87.6 - 69.1
5b = 18.5
b = 3.7

Thus, we have determined the exact numeric values of the constants b and c to be 3.7 and 4.1, respectively.